Résumé : Nucleosynthesis of fluorine in the context of helium burning occurs through the 15N(α,γ)19F reaction. At temperatures where fluorine formation takes place in most astrophysical models, the narrow resonance associated with the 4.378 MeV level of 19F is expected to dominate the reaction rate, but its strength is not known. We used a 15N confined gas target to study this level by means of the transfer reaction 15N(7Li,t)19F at 28 MeV. Reaction products were analysed with a split pole magnetic spectrometer and the angular distributions for the first 16 levels of 19F were extracted. These distributions are fairly well reproduced by FR-DWBA calculations in the framework of an γ-cluster transfer model with a compound-nucleus contribution obtained by Hauser-Feshbach calculations. α-spectroscopic factors were deduced and, for unbound levels, the α-widths were determined and compared with the existing direct measurements. The α-width of the level of astrophysical interest (Ex = 4.378 MeV) was found to be Γα = 1.5 × 10-9 eV, a value 60 times smaller than the commonly used one. The astrophysical consequences for 19F production in AGB stars are discussed.